TH-Collocation for the biharmonic equation

  • Authors:

  • Martín Díaz;Ismael Herrera

  • Affiliations:

  • Mexican Petroleum Institute(IMP) and Institute of Geophysics, National University of Mexico (UNAM), Apdo. Postal 22-582, Mexico 14000, Mexico D.F.;Institute of Geophysics, National University of Mexico (UNAM), Apdo. Postal 22-582, Mexico 14000, Mexico D.F.

  • Venue:
  • Advances in Engineering Software
  • Year:
  • 2005

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Abstract

This paper is intended as a contribution to enhance orthogonal collocation methods. In this, a novel collocation method--TH-collocation--is applied to the biharmonic equation and the merits of such procedure are exhibited. TH-collocation relaxes the continuity requirements and, for the 2D problems here treated, leads to the development of algorithms for which the matrices are sparse (nine-diagonal), symmetric and positive definite. Due to these properties, the conjugate gradient method can be directly, and more effectively, applied to them. These features contrast with those of the standard orthogonal spline collocation on cubic Hermites, which yields matrices that are non-symmetric and non-positive. This paper is part of a line of research in which a general and unified theory of domain decomposition methods, proposed by Herrera, is being explored. Two kinds of contributions can be distinguished in this; some that are relevant for the parallel computation of continuous models and new discretization procedures for partial differential equations. The present paper belongs to this latter kind of contributions.